Systematic and Unsystematic Risk and the Efficient Frontier

Spread your money across more and more shares and the risk of your portfolio falls, quickly at first and then more slowly, until it reaches a floor that no amount of further diversification can break. That floor exists because some risks hit every company together: a change in interest rates, a recession, a surge in inflation.

The risk that disappears as you add shares is the risk of individual companies going wrong in their own ways. The risk that remains is the risk of the market as a whole. This distinction is the most important idea in the theory of investment, because it decides which risk investors are paid for.

This topic explains systematic and unsystematic risk and why only the first earns a reward, how total risk divides into the two parts, how business and financial risk relate to them, the efficient portfolio and efficient frontier, the risk-free asset, the market portfolio and the capital market line, and the coefficient of variation as a decision rule, with worked examples.

The next topic uses these ideas to build the capital asset pricing model.

The different types of risk, including systematic business risk and systematic and unsystematic financial risk, were the subject of May Diet, 2026, Question 3(b) (10 marks). Read portfolio theory and diversification first.

Systematic and unsystematic risk

Unsystematic risk arises from uncertainties unique to a particular company or industry. Examples: a strike by its workers, a strong new competitor, the loss of a big contract, a rise in the duty on the company’s raw material, a failure to obtain supplies. It is also called unique, specific or diversifiable risk.

When assets that are not perfectly correlated are combined, the portfolio’s risk is less than the weighted sum of the individual risks, and the risk that disappears in this process is the unsystematic risk: good outcomes in some companies offset bad outcomes in others. Systematic risk arises from economy-wide uncertainties and the tendency of securities to move together with the market.

Examples: a change in the interest rate policy, heavy government deficit financing, rising inflation, a relaxation of foreign exchange controls, a change in tax rates. It is also called market or non-diversifiable risk, because there is nothing left to add to the portfolio that would offset it.

Total risk of a security is the variance or standard deviation of its returns and has two parts, systematic and unsystematic. For example, a share has a total standard deviation of 30% (variance 900). Its beta is 1.2 and the market’s standard deviation is 20% (variance 400). The systematic part of the variance is β²σ_m² = 1.44 × 400 = 576 (a standard deviation of 24%), and the unsystematic part is 900 − 576 = 324 (18%).

So 64% of its total risk is market-related and 36% unique and removable by diversification.

What follows for investors

• Investors expect a return above the risk-free rate in return for bearing risk.
• A holder of a single share bears both kinds of risk, so total risk matters to that investor.
• A well-diversified investor has eliminated the unsystematic risk, so total risk is irrelevant and no extra return is demanded for unsystematic risk. The only risk that earns a higher expected return is systematic risk.
• Shares of companies sensitive to the economy (luxury goods makers) have high systematic risk; shares of utilities, with steady demand, have low systematic risk. Systematic risk is measured by beta.

Business risk and financial risk

Business risk is the variability of operating profit that comes from the nature of the business (demand, costs, operating gearing). It has a systematic part (how much operating profit moves with the economy) and an unsystematic part (events unique to the firm).

Financial risk is the extra variability of the returns to shareholders caused by borrowing, because interest is a fixed charge: it increases the sensitivity of equity returns to the economy (systematic financial risk, shown in a higher equity beta for a more geared company) and adds the risk of default and distress that is specific to the company (unsystematic financial risk). The effect of gearing is the subject of later topics.

Efficient portfolios and the efficient frontier

An efficient portfolio is one that gives the highest expected return for its level of risk (or the lowest risk for its level of return). Of all the portfolios that can be made from risky assets, those that are efficient lie on a curve, the efficient frontier. A portfolio below it is dominated by another that gives more return for the same risk or less risk for the same return.

Because assets are not perfectly correlated, the frontier bows towards the upper left: combinations are better than single assets. Which portfolio on the frontier an investor chooses depends on risk aversion: a very risk-averse investor picks a low-risk, low-return point, a less risk-averse one a higher point.

The risk-free asset and the capital market line

A risk-free asset has a standard deviation of zero and no covariance with other assets. The market portfolio is a portfolio of all risky investments traded in the market (excluding risk-free securities), weighted by their market values.

Under the assumption that investors can lend or borrow at the risk-free rate, every investor holds some combination of the risk-free asset and the market portfolio, and the combinations lie on the capital market line (CML):

R_p = (1 − w_m)R_f + w_mR_m and σ_p = w_mσ_m

where w_m is the proportion in the market portfolio. Take R_f = 6%, R_m = 14% and σ_m = 20%. The slope of the line is (14 − 6) ÷ 20 = 0.4 for each point of risk.

• Lending:
  70% in the market and 30% in the risk-free asset: return 0.3 × 6 + 0.7 × 14 = 11.6%
  risk 0.7 × 20 = 14%.
• Borrowing:
  130% in the market funded by borrowing 30% at the risk-free rate: return −0.3 × 6 + 1.3 × 14 = 16.4%
  risk 1.3 × 20 = 26%.

Every point on the line satisfies R_p = 6 + 0.4σ_p: the extra 0.4% of return for each 1% of risk is the market’s reward for bearing risk. Portfolios on the line beat any other combination, which is why the market portfolio is the best risky portfolio for everyone.

Decision rule: the coefficient of variation

Choose the portfolio with the highest return and the lowest risk. When no portfolio is best on both, use the coefficient of variation = standard deviation ÷ expected return, the risk per unit of return, and choose the lowest. For portfolios X (return 12%, risk 15%), Y (10%, 9%) and Z (14%, 22%) the coefficients are 1.25, 0.90 and 1.57, so Y is preferred.

Assumptions of capital market theory

Investors can borrow and lend at the risk-free rate; they have the same expectations and a one-period horizon; assets are divisible; there are no taxes or transaction costs; there is no inflation and interest rates do not change; and markets are in equilibrium. Each is a simplification, and the theory is a model, not a description.

The ideas in more depth

Why the market does not pay for diversifiable risk

If a share carried a reward for its unique risk, investors could buy it, combine it with others to remove that risk, and earn the reward for nothing. Competition for such an opportunity pushes the price up and the expected return down until only the reward for market risk remains.

This is the reasoning that makes beta, and not the standard deviation, the measure of risk in the capital asset pricing model.

Why diversification has a floor

As more shares are added, the unique risk is averaged out, but the common sensitivity to the market remains. A rough illustration: a single share with a standard deviation of 40%, in a market whose standard deviation is 20%, might give a portfolio standard deviation of about 28% with five shares, 25% with ten, 23% with twenty and 22% with forty, approaching 20%.

The numbers are only illustrative, but the shape is real: most of the benefit comes from the first dozen or so shares.

Sources and references

• No accounting standard governs portfolio theory. The capital market line and the efficient frontier derive from the work of Markowitz and of Sharpe, Lintner and Tobin.

These points are stated as at 5 November 2026.

Worked examples

1. Systematic.
   1.2² × 400 = 576.
2. Unsystematic.
   900 − 576 = 324.

1. Return.
   0.3 × 6 + 0.7 × 14 = 11.6%.
2. Risk.
   0.7 × 20 = 14%.

1. Coefficient.
   9 ÷ 10 = 0.90.

How to answer in the exam

• Define both risks with examples and say which can be diversified.
• State which risk is rewarded and why, in terms of a diversified investor.
• For the capital market line, compute weights, return and risk separately.
• Link business and financial risk to the systematic and unsystematic parts.

Common mistakes in the exam

• Saying that diversification removes all risk.
• Giving examples of market-wide events as unsystematic risk (or the reverse).
• Using total risk for the pricing of a diversified investor’s holding.
• Forgetting that borrowing makes the weight in the market more than 100%.
• Choosing by return alone and ignoring the coefficient of variation.
• Taking the risk of the risk-free asset as positive.

Quick revision

• Total risk = systematic + unsystematic; unsystematic is diversifiable.
• Only systematic risk (beta) is rewarded for a diversified investor.
• CML: R_p = R_f + (R_m − R_f)σ_p ÷ σ_m.
• Coefficient of variation = standard deviation ÷ expected return; lowest wins.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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